1. Introduction. My articles in this volume illustrate two aspects of my work
a psychologically oriented mathematician. The present article shows elementary
mathematics in the service of psychology. The other article [1] shows elementary
psychology in the service of mathematics. Both papers bear on simple genetic
models: deterministic models in this paper and stochastic models in the other
one.

In psychology one frequently encounters facile evolutionary explanations of
contemporary behaviors and their neural substrates. It is often easy to convince
oneself that a certain characteristic of a currently predominant genotype permitted individuals of that genotype to have more offspring than conspecifics,
thus ensuring the success of the genotype. The (modest) interest in such exercises
is partially predicated on the validity of the transition between individual
reproductive success ("fitness") and long-term success of the genotype. This
paper shows that such transitions are not always valid.

2. Fitness and survival. According to E. O. Wilson, "Hamilton's theorem on
altruism consists merely of a more general restatement of the basic axiom that genotypes increase in frequency if their relative fitness is greater" [2, pp. 415-416,
italics added]. W. D. Hamilton's theory of the evolution of altruism will be
considered in §4. The present section relates to the italicized proposition, which
is an unusually explicit statement of a dominant theme of the literature of
Evolutionary Biology.

Consider the following example. Suppose that there are three interbreeding
varieties of zebras in a certain region. Call these varieties a, b, and c. They differ
in probability of survival from conception to reproductive age, perhaps because
of different diets. The common term for this survival probability is viability.
Assuming that all varieties are equally fertile, viability is proportional to, and
can thus be identified with, the expected number of offspring of a newly

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